Calculation method of flux measurements by static chambers · The linear method underestimates the flux even for short measurement times and without leakage of the chamber. • Using

Calculation method of flux measurements by static chambers

P.S. Kroon

Presented at the Calculation method chambers workshop, 16th – 18th March 2009, Helsinki, Finland

ECN-L--09-072 May 2009


Petra Kroon1,2

1. ECN, the Netherlands ; 2. TU Delft, the Netherlands

2 3-4-2009

3 3-4-2009

What’s the most appropriate method?

What’s the quality of a linear method?

4 3-4-2009

Outline•

Theoretical and simplified models

•

Comparison of the models

•

Arguments for linear model

•

Quality of chamber calculation methods

•

Summary and recommendations

•

Suggestions for calculation paper

•

Examples with Pumpeli data

•

Discussion

5 3-4-2009

Outline•

Theoretical and simplified models

•

Comparison of the models

•

Arguments for linear model

•

Quality of chamber calculation methods

•

Summary and recommendations

•

Suggestions for calculation paper

•

Examples with Pumpeli data

•

Discussion

6 3-4-2009

Theoretical models

Researcher Ca Cs0 Jg λ

De Mello and Hines (1994)

Ca(0)=Cair Constant Jg (t) Constant

Gao et al. (1998) Ca(0)=0 Constant Jg (t) Constant

Conen and Smith (2000)

Ca(0)=Cair Cs0 (t) Jg (t) Constant

Livingston et al. (2006)

Ca(t)=Cs0 (t)

Ca(0)=Cs0 (0)

Cs0 (t) Jg (t) λ(z)

Collar

Ca

Cs0

Flux Jg

Source λ

Soil Matrix

z0 =0

z=Z

1D diffusion equation

Mass balance

)(2

2

zzCD

tC λ+

∂∂

=∂∂

0=

=t

a

c dtdC

AVF

7 3-4-2009

Theoretical models

De Mello and Hines (1994), JGR

( )at

stcc

t

a

gc

CChF

dtdChJF

00

0

)0(

=

=

−=

==

Gao and Yates (1998), JGR

( ) ⎟⎠⎞

⎜⎝⎛−−=

⎟⎠⎞

⎜⎝⎛−−−=

=

=

tAV

hCChtJ

tAV

hCCCtC

tcat

stcg

tcat

ssa

/exp)(

/exp)()(

00

000

⎟⎠⎞

⎜⎝⎛−=

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−=

tAV

hChtJ

tAV

hCtC

tcstcg

tcsa

/exp)(

/exp1)(

0

0

stcc

t

a

gc

ChF

dtdChJF

0

0

)0(

=

===

hDha

tc

3/4θ=With

soilmairm

3

3

=>θ

8 3-4-2009

Theoretical models General behaviour of models based on Gao and Yates (1998) and De Mello and Hines (1994)

Gao and Yates (1998)

9 3-4-2009

Theoretical models General behaviour of models based on Gao and Yates (1998) and De Mello and Hines (1994)


t->∞ Ca(t)=Cs

0 & J

g(t)=0

10 3-4-2009

Theoretical models Conen and Smith (2000), European Journal of Soil Science


De Mello (1994) Ca(0)=Cair Constant Jg (t) ConstantGao (1998) Ca(0)=0 Constant Jg (t) ConstantConen

(2000) Ca(0)=Cair Cs0

(t) Jg

(t) ConstantLivingston (2005) Ca(t)=Cs

0 (t)Ca(0)=Cs

0 (0)Cs

0 (t) Jg (t) λ(z)

11 3-4-2009

Theoretical models Conen and Smith (2000), European Journal of Soil Science

12 3-4-2009

Theoretical models Conen and Smith (2000), European Journal of Soil Science ( ))()()( 0 tCtChtJ as

tcg −=

13 3-4-2009

Theoretical models Conen and Smith (2000), European Journal of Soil Science ( ))()()( 0 tCtChtJ as

tcg −=

t->∞ Ca(t)=Cs

0

(t)

& Jg

(t)=0

14 3-4-2009

Theoretical models Livingston et al. (2006), Soil science society of America journal


De Mello (1994) Ca(0)=Cair Constant Jg (t) ConstantGao (1998) Ca(0)=0 Constant Jg (t) ConstantConen (2000) Ca(0)=Cair Cs

0 (t) Jg (t) ConstantLivingston

(2006) Ca(t)=Cs0

(t)Ca(0)=Cs

0

(0)Cs

0

(t) Jg

(t) λ(z)

( ) ( )( )

tc

to

at

a

hAV

tetVAJCtC

/

1/erfc/2 /0

=

⎥⎦

⎤⎢⎣

⎡ −+⎟⎠⎞

⎜⎝⎛+= =

τ

ττπ

τ τ

15 3-4-2009

Theoretical models Differences in theoretical models:

•

Assumptions -> different equations for Ca(t) and Jg (t)

Similarity in theoretical models:•

Jg (t) is not constant•

No leakage taken into account•

No vegetation taken into account


De Mello and Hines (1994) Ca(0)=Cari Constant Jg (t) ConstantGao et al. (1998) Ca(0)=0 Constant Jg (t) ConstantConen and Smith(2000) Ca(0)=Cair Cs

0 (t) Jg (t) ConstantLivingston et al. (2006) Ca(t)=Cs

0 (t)Ca(0)=Cs

0 (0)Cs

0 (t) Jg (t) λ(z)

16 3-4-2009

Theoretical modelsKutzbach et al. (2007), Biogeosciences:

⎟⎠⎞

⎜⎝⎛ −+−=

=

==

++=+=

+++=

=

Leak3

2

320

321exp

Leak

)0(

)()exp()()()(

)()()()()(

KkdDp

Bp

ppAV

dtdC

AVF

ttpppttftc

tFtFtFtFtF

p

tc

Rpsoilc

εε

17 3-4-2009

Simplified models Linear model:(e.g. Ruser et al. 1998; Hendriks et al. 2007)

Quadratic model:(e.g. Wagner et al. 1997)

H-M model:(e.g. Hutchinson and Mosier, 1984)

)()()()( tbtattftc lin εε ++=+=

)()()()( 2qua tctbtattftc εε +++=+=

1Candfor t

ln)2)((

)(

12

0112

12

01

02101

201

>−−

=

⎥⎦

⎤⎢⎣

⎡−−

−−−−

=

CCCt

CCCC

CCCttACCVFc

0=

=t

a

c dtdC

AVF

Anthony et al. (1995)

18 3-4-2009

Simplified models Slope-intercept model:(Kroon et al. 2008)

0

3

6

9

0 400 800 1200 1600

t [s]

dC/d

t [pp

b/se

c]

ExpLin

1500

5500

9500

13500

0 400 800 1200 1600

t [s]

C [p

pb]

ExpLin

1N1,2,..,i1ii

1ii

i

−=−−

=−

−

ttCC

dtdC

( ) ( )ahJF

tbtahttfhtJ

gc

ling

.)0(

)(.)()(.)(

==

++=+= εε

19 3-4-2009

Comparison of the modelsLinear De Mello and Hines (1994)

⎟⎠⎞

⎜⎝⎛−−−= = t

AVhCCCtC tca

tssa

/exp)()( 000btatca +=)(

versus

Kroon et al. (2008)

Cum(Lin)/Cum(Exp):

69% and 63%

Based on measurements at Cabauw in the Netherlands

20 3-4-2009

Comparison of the modelsLinear Conen and Smith (2000)

btatca +=)(versus


(Lin flux)/(Real flux) range: 72% and 99%

Based on modelp

iii C

VAJ

CC ++= −−

11

21 3-4-2009

Comparison of the modelsIntercept De Mello and Hines (1994)

⎟⎠⎞

⎜⎝⎛−−−= = t

AVhCCCtC tca

tssa

/exp)()( 000

versus

Kroon et al. (2008)

Based on measurements at Cabauw in the Netherlands

1N1,2,..,i1ii

1ii

i

−=−−

=−

−

ttCC

dtdC

( )0..)0( bahJF gc +==0

)0(=

==t

a

gc dtdChJF

22 3-4-2009

Comparison of the modelsWhat’s the most accurate model?

•

Determination by goodness-of-fit analyses

( )∑=

−=N

1i

2ii

2 yyχ

( )tchAV /

=τFlux difference dependent on:

Livingston et al. (2006) Kroon et al. (2008)

23 3-4-2009

Why

do most of the people

still

use

a linear

regression?

Possible reasons:•

Assumption that concentration behaviour is linear over short measurement times.

•

Assumption that non-linear concentration behaviour can only be caused by leakage.

•

Assumption that uncertainty due to spatial and temporal variation is much larger than the biases due to linear regression.

24 3-4-2009

Assumption

I: Short measurement

times

Kroon et al. (2008)

25 3-4-2009

Assumption

II: Non-linearity

can

only

occur

due

to

leakage


Based on theoretical Gao model without leakage

26 3-4-2009

Assumption III: Uncertainty due to spatial and temporal variation is much

larger than biases due to linear regression

27 3-4-2009

Why

do most of the people

still

use

a linear

regression?

Possible reasons:•

Assumption that conentration behaviour is linear over short measurement times.

•

Assumption that non-linear concentration behaviour can only be caused by leakage.

•

Assumption that uncertainty due to spatial and temporal variation is much larger than the biases due to linear regression.

Assumptions are not definitely truth!

28 3-4-2009

Quality of chamber calculation methodsRochette and Eriksen-Hamel (2008)

29 3-4-2009

Quality chamber calculation methodsRochette and Eriksen-Hamel (2008)

30 3-4-2009

Quality chamber calculation methodsRochette and Eriksen-Hamel (2008)

31 3-4-2009

Summary•

There are several studies given in the literature for calculating fluxes by static chambers. They are based on the mass equation and diffusion equation. The models are based on different assumptions. However, they all indicate that the fluxes are not constant.

•

The concentration behaviour is dependent on the height of the chamber and the air filled porosity. Underestimation increases with decreasing height and increasing air filled porosity.

•

There are several simplified models for calculating fluxes by static chambers, like quadratic, linear and H-M model. These simplified models underestimate the flux. The amount of underestimation can be more than 40%.

32 3-4-2009

Summary•

The linear method underestimates the flux even for short measurement times and without leakage of the chamber.

•

Using an incorrect method leads to a systematic underestimation which is very significant even in comparison with the spatial and temporal variation.

•

The quality of the flux estimation is dependent on the used model, the amount of measurement points and measurement time.

33 3-4-2009

Recommendations•

A non-linear method should be used. Compare different non-linear methods using a goodness-of-fitanalyses to choose the most appropriate method.

•

Amount of measurement points should be at least 3.

•

The height of the chamber should be at least 40 cmhr-1.

*http://biogeo.botanik.uni-greifswald.de/index.php?id=264 (Lin&Non-linear)

**http://arsagsoftware.ars.usda.gov (Excell comparison Lin,Qua&NDFE)

Method References Model available onlineExp1 De Mello and Hines

(1994)Exp2 Gao et al. (1998)Exp3 Kutzbach et al. (2007) X*

NDFE Livingston et al. (2006) X**

Slope intercept Kroon et al. (2008)

34 3-4-2009

Suggestions for joint calculation paper

Possible research questions:

•

Which model/method should be used?

•

Which parameters characterize the amount of flux underestimation?

•

Is it possible to derive a correction algorithm?– For already published data– For flux estimates based on two samples

35 3-4-2009


Comparison of several models using a goodness-of-fit analyses

Method Theoretical/Simplified


Kutzbach et al. (2008)

Kroon et al. (2008)


De Mello and Hines

(1994)Exponential Theoretical X X XNDFE Theoretical XQuadratic Simplified X X?Linear Simplified X XIntercept Simplified X

Note:

• Check if the Pumpeli soil behaves

like a real soil.


De Mello and Hines (1994)

Ca(0)=Cair Constan t

Jg (t) Constant

Gao et al. (1998)

Ca(0)=0 Constan t

Jg (t) Constant


Ca(0)=Cair Cs0 (t) Jg (t) Constant


Ca(t)=Cs0 (t)

Ca(0)=Cs0 (

0)

Cs0 (t) Jg (t) λ(z)

36 3-4-2009


Validating the reliability of the following two hypotheses:

•

The smaller the h the larger the underestimation

•

The larger the air porosity the larger the underestimation


37 3-4-2009

Is it possible to derive a correction algorithm?

For example:•

Assume De Mello and Hines or Gao and Yates model are the most suitable method.

De Mello and Hines (1994), JGR Gao and Yates (1998), JGR

)(/

exp/1

/exp/)(

un0

un

0

tJCJ

tAV

hC

tAV

hJtJ

g

tc

tcg

=

⎟⎠⎞

⎜⎝⎛−=

⎟⎠⎞

⎜⎝⎛−=

( ) ⎟⎠⎞

⎜⎝⎛−−= = t

AVhCChtJ tca

ts

tcg /exp)( 00 ⎟

⎠⎞

⎜⎝⎛−= t

AVhChtJ tcs

tcg /exp)( 0

)(/

exp/1

/exp/)(

un0

un

0

tJCJ

tAV

hC

tAV

hJtJ

g

tc

tcg

=

⎟⎠⎞

⎜⎝⎛−=

⎟⎠⎞

⎜⎝⎛−=

38 3-4-2009

Examples Pumpeli

data

Comparison of several models using a goodness-of-fit analyses

Comparisons based on:• Radeks data (h=0.41 m)• Peters data (h=0.33 m)• Jespers data (h=0.058/0.0625/0.064 m)

Method Theoretical/Simplified


Kutzbach et al. (2008)

Kroon et al. (2008)


De Mello and Hines

(1994)Exponential Theoretical X X XNDFE Theoretical XQuadratic Simplified X X?Linear Simplified X XIntercept Simplified X

39 3-4-2009

Radek

All - Radekh=0.41 m

0%

100%

200%

300%

400%

500%

600%68 91 22

6

146

488

476

848

798

1633

1744 51 22

8

601

986

2353 52 18

3

453

745

1684

Flux CH4 (Lin Mari)

Met

hod/

Lin

[%]

QuadNDFE

Fine dry Coarse dry Fine wet

40 3-4-2009

Radek

All - Radekh=0.41 m

0

1

2

3

68 91 226

146

488

476

848

798

1633

1744 51 22

8

601

986

2353 52 18

3

453

745

1684

Flux CH4 (Lin Mari)

Fmea

s/Fp

ump

[-]

QuadNDFELin


Ove

rest

imat

ion

Und

eres

timat

ion

41 3-4-2009

RadekRadek - Fine dry

Flux 6

y = 1.925x + 2.2623R2 = 0.9941

2

2.3

2.6

2.9

3.2

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount

Flin/Fpump: 0.83Fquad/Fpump: 0.98FNDFE/Fpump: 1.11

Radek - Coarse dryFlux 15

y = 9.4742x + 2.2822R2 = 0.9891

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount


Radek - Fine wetFlux 18

y = 1.832x + 2.0694R2 = 0.9952

2

2.25

2.5

2.75

3

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount


Radek - Fine dryFlux 4

y = 0.5876x + 2.3057R2 = 0.9867

2.2

2.3

2.4

2.5

2.6

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount


42 3-4-2009


Flux 6

y = 1.925x + 2.2623R2 = 0.9941

2

2.3

2.6

2.9

3.2

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 9.4742x + 2.2822R2 = 0.9891

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 1.832x + 2.0694R2 = 0.9952

2

2.25

2.5

2.75

3

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 0.5876x + 2.3057R2 = 0.9867

2.2

2.3

2.4

2.5

2.6

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount


NDFE

NDFE

Quad

Lin

43 3-4-2009


Flux 6

y = 1.925x + 2.2623R2 = 0.9941

2

2.3

2.6

2.9

3.2

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 9.4742x + 2.2822R2 = 0.9891

0

2

4

6

8

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 1.832x + 2.0694R2 = 0.9952

2

2.25

2.5

2.75

3

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount



y = 0.5876x + 2.3057R2 = 0.9867

2.2

2.3

2.4

2.5

2.6

0 0.1 0.2 0.3 0.4 0.5

Time

CH

4 am

ount


NDFE

NDFE

Quad

Lin

What’s the most appropriate method?

44 3-4-2009

RadekFlux number Soil Level Ratio Lin Ratio Quad Ratio NDFE X2 Lin X2 Quad X2 NDFE Equal

1 fine, dry 1 0.95 0.74 0.97 4.25E-04 4.02E-04 4.27E-042 fine, dry 1 1.28 0.24 0.99 4.18E-04 1.91E-04 4.25E-043 fine, dry 2 0.95 1.05 1.05 9.44E-04 8.71E-04 9.20E-04 14 fine, dry 2 0.64 0.83 1.02 4.84E-04 2.07E-04 2.56E-045 fine, dry 3 0.82 1.01 0.84 3.77E-03 1.88E-03 3.60E-03 16 fine, dry 3 0.83 0.97 1.11 2.19E-03 1.26E-03 1.28E-03 17 fine, dry 4 0.88 0.77 0.89 7.34E-03 5.44E-03 7.61E-038 fine, dry 4 0.87 0.90 0.88 2.11E-02 2.10E-02 2.10E-029 fine, dry 5 0.75 0.86 0.88 4.90E-02 4.11E-02 4.52E-0210 fine, dry 5 0.84 1.06 0.91 6.39E-02 3.81E-02 111 coarse, dry 1 0.95 1.40 0.96 1.56E-04 9.03E-05 1.54E-0412 coarse, dry 2 1.06 1.19 1.23 1.06E-03 9.50E-04 1.00E-0313 coarse, dry 3 0.93 0.79 0.93 1.97E-03 7.64E-04 1.98E-0314 coarse, dry 4 0.86 1.07 0.88 1.13E-02 3.72E-03 1.05E-02 115 coarse, dry 5 1.03 1.44 2.06 1.06E-01 7.48E-03 4.60E-0316 fine, wet 117 fine, wet 2 1.16 1.32 1.21 1.98E-04 1.22E-04 1.76E-0418 fine, wet 3 0.98 1.20 1.00 1.68E-03 2.07E-04 1.54E-0319 fine, wet 4 0.73 0.74 0.74 2.34E-03 2.33E-03 2.35E-03 1

20 fine, wet 5 0.95 0.98 0.96 4.28E-03 3.63E-03 4.07E-03 1Total 5 8 10 7

Average 0.92 0.98 1.03 1.47E-02 6.82E-03 5.95E-03

45 3-4-2009

Peter (filtered red boxes in concentration)

All - Peterh=0.33 m

0%

100%

200%

300%

400%

500%

600%76 65 27

1

234

602

558

1020 95

3

2219

2002

1021 99

8

2031

1954 82 77 22

6

206

596

559

Flux CH4 (Lin Mari)

Met

hod/

Lin

[%]

QuadNDFE

Fine dry Coarse dry

46 3-4-2009

Peter (filtered red boxes in concentration)

All - Peterh=0.33 m

0

1

2

3

76 65 271

234

602

558

1020 95

3

2219

2002

1021 99

8

2031

1954 82 77 22

6

206

596

559

Flux CH4 (Lin Mari)

Fmea

s/Fp

ump

[-]

QuadNDFELin

Fine dry Coarse dry

Ove

rest

imat

ion

Und

eres

timat

ion

47 3-4-2009

Peter (filtered red boxes in concentration)Flux number Soil Level Ratio Lin Ratio Quad Ratio NDFE X2 Lin X2 Quad X2 NDFE Equal

1 fine, dry 12 fine, dry 13 fine, dry 24 fine, dry 2 0.91 0.99 0.93 4.48E-04 3.48E-04 4.13E-04 15 fine, dry 36 fine, dry 3 0.86 0.99 1.14 2.20E-03 2.67E-04 1.96E-047 fine, dry 4 1.02 1.19 1.35 8.57E-03 4.75E-04 3.16E-048 fine, dry 4 1.00 1.19 1.44 9.89E-03 1.11E-03 4.90E-049 fine, dry 5 1.04 1.19 1.10 3.55E-02 1.22E-0210 fine, dry 5 0.99 1.11 1.21 2.21E-02 7.07E-03 8.81E-0311 coarse, dry 4 0.98 1.20 1.00 1.36E-02 6.66E-04 1.24E-0212 coarse, dry 4 1.00 1.20 1.50 1.26E-02 4.18E-03 2.33E-0313 coarse, dry 5 0.91 1.01 1.15 2.95E-02 1.60E-02 1.18E-0214 coarse, dry 5 0.92 1.09 1.26 4.41E-02 8.76E-03 1.15E-0215 coarse, dry 116 coarse, dry 117 coarse, dry 2 0.99 1.22 1.01 1.26E-03 6.19E-04 1.21E-0318 coarse, dry 2 0.84 0.87 0.86 1.27E-04 1.13E-04 1.17E-04 120 coarse, dry 3 0.78 0.96 0.80 6.47E-03 1.47E-03 5.85E-03 1

21 coarse, dry 3 0.77 0.88 0.78 1.89E-02 1.74E-02 1.87E-02 1Total 7 6 2 4

Average 0.93 1.08 1.11 1.47E-02 5.05E-03 5.71E-03

48 3-4-2009

Jesper

All - Jesperh=0.058/0.0625/0.064 m

0%

100%

200%

300%

400%

500%

600%21 15 33 31 16

3

141

139

216

664

565 24 20 71 69 183

211

266

387 19 18 64 59

Flux CH4 (Lin Mari)

Met

hod/

Lin

[%]

QuadNDFE


49 3-4-2009

Jesper

All - Jesperh=0.058/0.0625/0.064 m

0

1

2

3

21 15 33 31 163

141

139

216

664

565 24 20 71 69 183

211

266

387 19 18 64 59

Flux CH4 (Lin Mari)

Fmea

s/Fp

ump

[-]

QuadNDFELin


Ove

rest

imat

ion

Und

eres

timat

ion

50 3-4-2009

JesperJesper - Coarse dry

Flux 14

y = 1.65x + 2.5248R2 = 0.9493

1

2

3

4

0.00 0.10 0.20 0.30 0.40 0.50

Time [hr]

CH

4 am

ount


Jesper - Fine wetFlux 22

y = 1.3549x + 2.7993R2 = 0.8897

1

2

3

4

0.00 0.10 0.20 0.30 0.40 0.50

Time [hr]

CH

4 am

ount


Jesper - Coarse dryFlux 18

y = 9.2705x + 2.6414R2 = 0.8361

1

3

5

7

9

0.00 0.10 0.20 0.30 0.40 0.50

Time [hr]

CH

4 am

ount


Jesper - Fine dryFlux 8

y = 5.6125x + 3.9041R2 = 0.9268

3

4

5

6

7

0.00 0.10 0.20 0.30 0.40 0.50

Time [hr]

CH

4 am

ount


51 3-4-2009

JesperFlux number Soil Level Ratio Lin Ratio Quad Ratio NDFE X2 Lin X2 Quad X2 NDFE Equal

1 fine, dry FL1a_lin 0.16 0.23 0.16 7.03E-04 6.65E-05 6.63E-04 12 fine, dry FL1b_lin 0.11 0.31 0.12 5.22E-03 8.50E-05 5.13E-03 13 fine, dry FL2a_lin 0.14 0.27 0.15 1.29E-02 5.60E-03 14 fine, dry FL2b_lin 0.13 0.23 0.14 6.22E-03 1.81E-03 6.04E-03 15 fine, dry FL3a_lin 0.16 0.29 0.16 1.38E-01 6.97E-03 16 fine, dry FL3b_lin 0.14 0.26 0.15 9.64E-02 2.45E-03 17 fine, dry FL4a_lin 0.09 0.09 0.09 6.36E-02 6.24E-02 6.36E-02 18 fine, dry FL4b_lin 0.15 0.30 0.16 3.25E-01 1.32E-02 19 fine, dry FL5a_lin 0.16 0.31 0.17 2.97E+00 5.01E-02 110 fine, dry FL5b_lin 0.15 0.28 0.15 2.42E+00 2.89E-01 111 coarse, dry FL1a_lin 0.11 0.18 0.11 2.70E-03 6.90E-04 2.63E-03 112 coarse, dry FL1b_lin 0.09 0.11 0.10 2.26E-04 1.11E-04 1.92E-04 113 coarse, dry FL2a_lin 0.14 0.30 0.14 3.79E-02 4.00E-04 114 coarse, dry FL2b_lin 0.14 0.25 0.14 1.75E-02 3.34E-04 1.68E-02 115 coarse, dry FL3a_lin 0.24 0.44 0.25 1.62E-01 2.97E-04 116 coarse, dry FL3b_lin 0.29 0.57 0.30 2.69E-01 1.65E-02 117 coarse, dry FL4a_lin 0.23 0.47 0.24 5.04E-01 3.10E-03 118 coarse, dry FL4b_lin 0.35 0.84 0.36 2.02E+00 1.66E-01 119 wet, fine FL1a_lin 0.10 0.17 0.10 1.80E-03 4.35E-04 1.76E-03 120 wet, fine FL1b_lin 0.09 0.20 0.10 3.01E-03 1.54E-04 2.92E-03 121 wet, fine FL2a_lin 0.16 0.27 0.16 1.62E-02 3.08E-03 1.57E-02 122 wet, fine FL2b_lin 0.15 0.30 0.81 2.73E-02 6.32E-03 1.30E-02

Total 1 21 1 21Average 0.16 0.30 0.19 4.14E-01 2.86E-02 1.17E-02

52 3-4-2009

Summary examples

Ratios based on all measurement points:

• Shall we perform all these analyses for all data and with all models?

Name Height [m] Lin/Pump Quad/Pump NDFE/Pump

Jesper 0.06 0.16 0.30 0.19

Peter 0.33 0.93 1.08 1.11

Radek 0.47 0.92 0.98 1.03

53 3-4-2009

Discussion: Suggestions for calculation paper

Possible research questions:

•


•


•

Is it possible to derive a correction algorithm?– For already published data– For flux estimates based on two samples


Petra Kroon1,2

1. ECN, the Netherlands ; 2. TU Delft, the Netherlands

55 3-4-2009

PeterAll - Peterh=0.33 m

100%

200%

300%

400%

500%

600%

76 65 271

234

602

558

1020 953

2219

2002

1021 998

2031

1954 82 77 226

206

596

559

Flux CH4 (Lin Mari)

Met

hod/

Lin

[%]

QuadNDFE

Fine dry Coarse dry

56 3-4-2009

Peter

All - Peterh=0.33 m

0

1

2

3

76 65 271

234

602

558

1020 95

3

2219

2002

1021 99

8

2031

1954 82 77 22

6

206

596

559

Flux CH4 (Lin Mari)

Fmea

s/Fp

ump

[-]

QuadNDFELin

Fine dry Coarse dry

57 3-4-2009

PeterFlux number Soil Level Ratio Lin Ratio Quad Ratio NDFE X2 Lin X2 Quad X2 NDFE Equal

1 fine, dry 1 0.95 1.08 0.97 8.89E-05 6.80E-05 8.51E-05 12 fine, dry 1 0.83 0.44 0.85 5.52E-04 3.31E-04 5.69E-043 fine, dry 2 1.01 1.36 2.13 3.15E-03 1.10E-03 8.77E-044 fine, dry 2 0.91 0.99 0.93 4.48E-04 3.48E-04 4.13E-04 15 fine, dry 3 0.88 1.03 0.91 1.17E-02 9.07E-03 1.12E-02 16 fine, dry 3 0.86 0.99 1.14 2.20E-03 2.67E-04 1.96E-047 fine, dry 4 1.02 1.19 1.35 8.57E-03 4.75E-04 3.16E-048 fine, dry 4 1.00 1.19 1.44 9.89E-03 1.11E-03 4.90E-049 fine, dry 5 1.04 1.19 1.10 3.55E-02 1.22E-0210 fine, dry 5 0.99 1.11 1.21 2.21E-02 7.07E-03 8.81E-0311 coarse, dry 4 0.98 1.20 1.00 1.36E-02 6.66E-04 1.24E-0212 coarse, dry 4 1.00 1.20 1.50 1.26E-02 4.18E-03 2.33E-0313 coarse, dry 5 0.91 1.01 1.15 2.95E-02 1.60E-02 1.18E-0214 coarse, dry 5 0.92 1.09 1.26 4.41E-02 8.76E-03 1.15E-0215 coarse, dry 1 0.75 1.66 0.77 4.19E-03 1.78E-03 4.14E-0316 coarse, dry 1 0.73 2.22 0.13 2.02E-02 9.46E-03 2.02E-0217 coarse, dry 2 0.99 1.22 1.01 1.26E-03 6.19E-04 1.21E-0318 coarse, dry 2 0.84 0.87 0.86 1.27E-04 1.13E-04 1.17E-04 120 coarse, dry 3 0.78 0.96 0.80 6.47E-03 1.47E-03 5.85E-03 1

21 coarse, dry 3 0.77 0.88 0.78 1.89E-02 1.74E-02 1.87E-02 1Total 9 7 5 5

Average 0.91 1.14 1.07 1.22E-02 4.63E-03 5.86E-03

Documents

Calculation method of flux measurements by static chambers · The linear method underestimates the flux even for short measurement times and without leakage of the chamber. • Using